Sampling as modulation - new technical article

When we digitize an electrical waveform - or a camera image - we "sample" the phenomenon at regular intervals of time or space, as appropriate. The Nyquist-Shannon sampling theorem tells us that if the rate of sampling is greater than twice the highest frequency contained in the variation of the phenomenon, the collection of sample values completely "describes" the variation. The corollary is that from the collection of sample values, we can precisely reconstruct the whole pattern of variation (the waveform, image or whatever).

The process of sampling can be looked at as a case of amplitude modulation. Here, the phenomenon to be captured is the modulating signal. The carrier, rather than being a sine wave (as in familiar radio modulation), is a series of narrow pulses at the sampling rate.

By looking at sampling as amplitude modulation, we can use familiar understandings of the frequency content of a modulated signal to understand the frequency content of the set of sample values, the way in which a reconstruction filter can reconstruct the original phenomenon from the set of samples, and how aliasing occurs.

This outlook and the insights we can get through it are described in my new technical article. "Sampling as Modulation", available here:

http://dougkerr.net/Pumpkin#SamplingModulation

Just a warning. Carla, who copy edited this piece, tells me that of all the technical manuscripts of mine she had edited over the years, this was the dullest.

Best regards,

Doug

Doug Kerr said:

Just a warning. Carla, who copy edited this piece, tells me that of all the technical manuscripts of mine she had edited over the years, this was the dullest.Doug

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Oh, I don't know about that Doug, but it may be rather deep for the holiday, generally speaking. I'm an ex-ham radio nut and managed to get to page five before remembering that I intended to change the furnace filter some time today.

Totally off topic, sorry, but have you ever considered writing an essay about railroad engine diesel/electric propulsion? I've been meaning to ask you about this for quite a while.

Hi, Tom,

Tom Robbins said:

Oh, I don't know about that Doug, but it may be rather deep for the holiday, generally speaking. I'm an ex-ham radio nut and managed to get to page five before remembering that I intended to change the furnace filter some time today.

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I understand.

What is really amazing is that Carla has essentially no technical background at all, and yet is very insightful about finding literary, syntactic, and sometimes even logical flaws in the manuscripts.

Totally off topic, sorry, but have you ever considered writing an essay about railroad engine diesel/electric propulsion? I've been meaning to ask you about this for quite a while.

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No, I haven't, but it is indeed a fascinating topic, and I may want to take it on. I've looked into some particular corners of it from time to time, but only on a limited basis.

There are wonderful mechanical as well as electrical aspects to it (nose-mounted motors and all that).

A related and equally fascinating field is the matter of electric streetcar propulsion in the "old days", with the mysteries of the various series/parallel transitions (including "bridge", "short-circuit", etc.).

Thanks for your thoughts.

Best regards,

Doug

Hi Doug,

I meant no disrespect with regard to sampling as modulation, of course. My understanding is due solely to my neanderthal point of view. Luddites unite; occupy the world! Heh-heh.

Speaking of cavemen, I discovered this little scene yesterday while rambling in the woods -



It would be great if you can find some time to investigate and write an essay about locomotive propulsion. As with many of the subjects you've written about, this topic became fascinating only after some years of photographic effort and subsequent pondering. Odd how often the two go together, isn't it?